61 research outputs found
Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments
We investigate the evolution of entanglement in multiple-quantum (MQ) NMR
experiments in crystals with pairs of close nuclear spins-1/2. The initial
thermodynamic equilibrium state of the system in a strong external magnetic
field evolves under the non-secular part of the dipolar Hamiltonian. As a
result, MQ coherences of the zeroth and plus/minus second orders appear. A
simple condition for the emergence of entanglement is obtained. We show that
the measure of the spin pair entanglement, concurrence, coincides qualitatively
with the intensity of MQ coherences of the plus/minus second order and hence
the entanglement can be studied with MQ NMR methods. We introduce an
Entanglement Witness using MQ NMR coherences of the plus/minus second order.Comment: 5 pages, 2 figure
Multiple Quantum NMR and Entanglement Dynamics in Dipolar Coupling Spin
We investigate numerically the time dependence of the multiple quantum
coherences and entanglement in linear chains up to nine nuclear spins of 1/2
coupled by the dipole-dipole interactions. Two models are considered: (1) a
spin chain with nearest-neighbor dipole -dipole interactions; (2) a more
realistic model with interactions between all spins. It is shown that the
entangled states appear between remote particles which do not interact directly
(model 1), while the interaction between all spins (model 2) not always results
in entanglement between remote spins.Comment: 14 pages, 3 figures. accepted for publication in Physical Review
Exact results on spin dynamics and multiple quantum dynamics in alternating spin-1/2 chains with XY-Hamiltonian at high temperatures
We extend the picture of a transfer of nuclear spin-1/2 polarization along a
homogeneous one-dimensional chain with the XY-Hamiltonian to the inhomogeneous
chain with alternating nearest neighbour couplings and alternating Larmor
frequencies. To this end, we calculate exactly the spectrum of the spin-1/2
XY-Hamiltonian of the alternating chain with an odd number of sites. The exact
spectrum of the XY-Hamiltonian is also applied to study the multiple quantum
(MQ) NMR dynamics of the alternating spin-1/2 chain. MQ NMR spectra are shown
to have the MQ coherences of zero and second orders just as in the case
of a homogeneous chain. The intensities of the MQ coherences are calculated.Comment: 10 pages, 4 figure
The multiple quantum NMR dynamics in systems of equivalent spins with the dipolar ordered initial state
The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with
the dipolar ordered initial state is considered. The high symmetry of the MQ
Hamiltonian is used in order to develop the analytical and numerical methods
for an investigation of the MQ NMR dynamics in the systems consisting of
hundreds of spins from "the first principles". We obtain the dependence of the
intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR
coherences) for the systems of spins. It is shown that these
profiles may be well approximated by the exponential distribution functions. We
also compare the MQ NMR dynamics in the systems of equivalent spins having two
different initial states, namely the dipolar ordered state and the thermal
equilibrium state in the strong external magnetic field.Comment: 11 pages 4 figure
Non-Ergodic Nuclear Depolarization in Nano-Cavities
Recently, it has been observed that the effective dipolar interactions
between nuclear spins of spin-carrying molecules of a gas in a closed
nano-cavities are independent of the spacing between all spins. We derive exact
time-dependent polarization for all spins in spin-1/2 ensemble with spatially
independent effective dipolar interactions. If the initial polarization is on a
single (first) spin, then the exact spin dynamics of the model is
shown to exhibit a periodical short pulses of the polarization of the first
spin, the effect being typical of the systems having a large number, , of
spins. If , then within the period () for odd (even)
-spin clusters, with standing for spin coupling, the polarization of
spin 1 switches quickly from unity to the time independent value, 1/3, over the
time interval about , thus, almost all the time, the spin 1
spends in the time independent condition . The period and the
width of the pulses determine the volume and the form-factor of the ellipsoidal
cavity. The formalism is adopted to the case of time varying nano-fluctuations
of the volume of the cavitation nano-bubbles. If the volume is varied by
the Gaussian-in-time random noise then the envelope of the polarization peaks
goes irreversibly to 1/3. The polarization dynamics of the single spin exhibits
the Gaussian (or exponential) time dependence when the correlation time of the
fluctuations of the nano-volume is larger (or smaller) than the , where the is the variance of the
coupling. Finally, we report the exact calculations of the NMR line shape for
the -spin gaseous aggregate.Comment: 26 pages, 3 figure
Fluctuations of Quantum Entanglement
It is emphasized that quantum entanglement determined in terms of the von
Neumann entropy operator is a stochastic quantity and, therefore, can
fluctuate. The rms fluctuations of the entanglement entropy of two-qubit
systems in both pure and mixed states have been obtained. It has been found
that entanglement fluctuations in the maximally entangled states are absent.
Regions where the entanglement fluctuations are larger than the entanglement
itself (strong fluctuation regions) have been revealed. It has been found that
the magnitude of the relative entanglement fluctuations is divergent at the
points of the transition of systems from an entangled state to a separable
state. It has been shown that entanglement fluctuations vanish in the separable
states.Comment: 5 pages, 4 figure
Asymmetry of bipartite quantum discord
It is known from the analysis of the density matrix for bipartite systems
that the quantum discord (as a measure of quantum correlations) depends on the
particular subsystem chosen for the projective measurements. We study asymmetry
of the discord in a simple physical model of two spin-1/2 particles with the
dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous
magnetic field. The dependence of the above discord asymmetry on the Larmour
frequencies at both T=0 (the ground state) and has been investigated. It
is demonstrated, in particular, that the asymmetry is negligible for high
temperatures but it may become significant with the decrease in temperature.Comment: 5 pages 3 figure
NMR Simulation of an Eight-State Quantum System
The propagation of excitation along a one-dimensional chain of atoms is
simulated by means of NMR. The physical system used as an analog quantum
computer is a nucleus of 133-Cs (spin 7/2) in a liquid crystalline matrix. The
Hamiltonian of migration is simulated by using a special 7-frequency pulse, and
the dynamics is monitored by following the transfer of population from one of
the 8 spin energy levels to the other.Comment: 10 pages, 3 figure
Entanglement in nuclear quadrupole resonance
Entangled quantum states are an important element of quantum information
techniques. We determine the requirements for states of quadrupolar nuclei with
spins >1/2 to be entangled. It was shown that entanglement is achieved at low
temperature by applying a magnetic field to a quadrupolar nuclei possess
quadrupole moments, which interacts with the electricfield gradient produced by
the charge distribution in their surroundings.Comment: 9 pages, 5 figure
Multiple-Quantum Spin Dynamics of Entanglement
Dynamics of entanglement is investigated on the basis of exactly solvable
models of multiple-quantum (MQ) NMR spin dynamics. It is shown that the time
evolution of MQ coherences of systems of coupled nuclear spins in solids is
directly connected with dynamics of the quantum entanglement. We studied
analytically dynamics of entangled states for two- and three-spin systems
coupled by the dipole-dipole interaction. In this case dynamics of the quantum
entanglement is uniquely determined by the time evolution of MQ coherences of
the second order. The real part of the density matrix describing MQ dynamics in
solids is responsible for MQ coherences of the zeroth order while its imaginary
part is responsible for the second order. Thus, one can conclude that dynamics
of the entanglement is connected with transitions from the real part of the
density matrix to the imaginary one and vice versa. A pure state which
generalizes the GHZ and W states is found. Different measures of the
entanglement of this state are analyzed for three-partite systems.Comment: 11 pages, 4 figure
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